The initial discovery of x-rays by Röntgen in 1895 [W. C. Röntgen, “Eine Neue Art von Strahlen” (Wurzburg Verlag, 1896); “On a New Kind of Rays,” Nature, Vol. 53, pp. 274-276 (Jan. 23, 1896)] occurred when Röntgen was experimenting with electron bombardment of targets in vacuum tubes. The contrast between the absorption from bone containing calcium (atomic number Z=20) and soft tissue containing mostly carbon (Z=6), was immediately apparent because the absorption difference between the two materials at x-ray energies between 5 and 30 keV can differ by a factor of 10 or more, as illustrated in FIG. 1. These high energy, short wavelength photons are now routinely used for medical applications and diagnostic evaluations, as well as for security screening, industrial inspection, quality control and failure analysis, and for scientific applications such as crystallography, tomography, x-ray fluorescence analysis and the like.
Although x-ray shadowgraphs have become a standard medical diagnostic tool, there are problems with simple absorption contrast imaging. Notably, for tests such as mammograms, variations in biological tissue may result in only a subtle x-ray absorption image contrast, making unambiguous detection of tumors or anomalous tissue difficult.
In the past decade, a new kind of x-ray imaging methodology has emerged, based on x-ray phase contrast interferometry. The method relies on the well-known Talbot interference effect, originally observed in 1837 [H. F. Talbot, “Facts relating to optical science No. IV”, Philos. Mag. vol. 9, pp. 401-407, 1836] and fully explained by Lord Rayleigh in 1881 [Lord Rayleigh, “On copying diffraction gratings and some phenomena connected therewith,” Philos. Mag. vol. 11, pp. 196-205 (1881)].
This effect is illustrated in FIG. 2. For an absorbing grating G of period p, the diffraction pattern from a monochromatic beam of a wavelength λ with sufficient coherence forms a repeating interference pattern that reconstructs the original grating pattern, (known as a “self-image”) at multiples of a distance known as the Talbot Distance DT. For the case when the incident beam is a plane wave (equivalent to a source located at infinity from the grating G), DT is given by:
                              D          T                =                              2            ⁢                          p              2                                λ                                    [                  Eqn          .                                          ⁢          1                ]            
Between the grating G and the Talbot Distance, other periodic interference patterns emerge as well. The periodicity and the position of the Talbot fringes depend on the transmission properties of the grating G, including amount of phase-shift and percent of absorption, and grating line-to-space (opening) ratio, or duty factor. For example, for a periodic absorption grating, a fringe pattern that reconstructs the original grating pattern with a lateral shift by half the grating period occurs at half the Talbot Distance DT/2, and a fringe pattern with a period of half of the original grating period occurs at one quarter of the Talbot Distance DT/4 and at three quarters of the Talbot Distance 3DT/4, as illustrated in FIG. 2. These 2-D interference patterns are sometimes called a “Talbot Carpet” because of the resemblance of these complex patterns to ornate oriental carpets. [Note: this image of an Optical Talbot Carpet in FIG. 2 is adapted from a file created by Ben Goodman and available at commons.wikimedia.org/wiki/File:Optical_Talbot_Carpet.png.]
FIGS. 3 and 4 illustrate a prior art Talbot interferometric comprising a partially coherent source 200 (shown as a microfocus source) of x-rays 288 and a beam splitting grating G1 210 of period p1 that establishes a set of Talbot interference fringe patterns 289. It should be noted that the coherence length of the x-ray source is preferably set to be comparable to or larger than the period p1 of the beam splitting grating G1 210, so that the Talbot interference fringes will have high contrast (Talbot fringes may be well defined if the fringe contrast is, for example, greater than 20%). The beam splitting grating 210 may be an amplitude (also known an absorption or transmission) grating, creating intensity fringes as illustrated in FIG. 2, but is more typically a phase grating for efficient use of the illuminating x-rays, introducing periodic phase-shifts to the x-ray pattern that also form periodic Talbot fringes 289. Henceforth in this application, a transmission grating will be used to describe gratings in which the x-ray transmission through the grating lines is less than 10% and a phase grating will be used to describe gratings in which the phase shift through the grating lines is a fraction (e.g. ½) or odd integer multiple of π.
The Talbot fringes 289 are detected using an x-ray detector 290, preferably with a spatial resolution equal to or better than one third of the Talbot fringe period and having a high x-ray quantum detection efficiency. The detector 290 transforms the x-ray intensity pattern into electronic signals that are transmitted over a connector 291 to an image processing system 295. When an object is placed in the beam path, the image processing system 295 is used to process the x-ray intensity pattern intensity information 298 to obtain absorption, phase, and scattering contrast images.
In practice, the spatial resolution of the detector 290 (such as a flat panel detector, or a charge coupled device (CCD) detector coupled with a scintillator that converts x-rays to visible light) is often on the order of tens of micrometers or larger, and the Talbot fringes 289 may be too fine to detect directly with the detector 290. In this case, an analyzer grating G2 220 of period p2 is often used to produce Moiré fringes. To record a complete set of images, the analyzer grating G2 220 will be moved in predetermined distances orthogonal to the grating period and relative to the detector to collect multiple interference patterns in a process called “phase-stepping”, or less commonly, rotated at a small angle relative to G1 to obtain a Moiré pattern in a single-shot image for Fourier analysis. The image(s) are then processed to reconstruct the wavefront and determine the shapes, structures, and composition of the objects that created them.
It should also be noted that, instead of physically moving the analyzer grating 220, the position of the x-ray source may also be displaced to create a translation of the interference images that allows the collection of phase-shift information. This can be accomplished electronically by moving the position of the electron beam that bombards the x-ray generating material that serves as the source for the x-rays [see, for example, H. Miao et al., “Motionless phase stepping in X-ray phase contrast imaging with a compact source”, Proceedings of the National Academy of Sciences, vol. 110(48) pp. 19268-19272, 2013] or by physically moving the x-ray source relative to a fixed position of the analyzer grating 220.
These grating-based x-ray phase-contrast imaging (XPCI) techniques are generally referred to as “grating-based interferometry” (GBI).
As illustrated so far, the grating interferometer only produces interference fringes, and the analysis of these fringes will reveal the structure of the already known grating G1 210 or the wavefront of the illumination beam. However, when an object is introduced in the path of the x-ray beam, variations in the wavefront introduced by the object result in corresponding changes in the pattern of the Talbot interference fringes, generally known as Moiré fringes. Interferometric image reconstruction techniques may then be used to analyze the wavefront and reconstruct images representing the structure of the unknown object.
In FIG. 5, the prior art Talbot interferometer of FIGS. 3 and 4 is illustrated being used as an imaging technique for a biological sample, in this case, a mouse 240-M, placed between the source 200 and the beam splitting grating G1 210. The x-rays 288 from the coherent source 200 pass through the mouse 240-M and the beam splitting grating G1 210 and create a perturbed set of Talbot fringes 289-M. The local phase shifts create angular deviations that translate into changes of locally transmitted intensity when analyzed by the analyzer grating G2 220 and detector 290. Collecting multiple images from the x-ray detector 290 for situations where the analyzer grating G2 220 has been displaced by multiple predetermined positions allow a recording of the interference pattern 289-M.
As before, the detector 290 transforms the x-ray intensity pattern into electronic signals that are transmitted over a connector 291 to an image processing system 295 used to produce one or more images 298-M with absorption, differential phase, phase, and scattering contrast information. Numerical processing of the images, including images collected by the system with and without the object under investigation, can be used to infer the shapes and structure of the objects that created them, including objects such as the mouse 240-M. The recorded intensity oscillations can be represented by a Fourier series, and with the proper image processing algorithms, differential phase shift and absorption signals can be extracted, and images corresponding to x-ray absorption, phase contrast, and scattering by the object can be synthesized. [See, for example, A. Momose et al., “Demonstration of x-ray Talbot interferometry”, Jpn. J. Appl. Phys. vol. 42, pp. L866-L868, 2003; A. Momose, U.S. Pat. No. 7,180,979, issued Feb. 20, 2007; T. Weitkamp et al. “Hard X-ray phase imaging and tomography with a grating interferometer”, Proc. SPIE vol 5535, pp. 137-142, 2004, and “X-ray phase imaging with a grating interferometer”, Optics Express vol. 13(16), pp. 6296-6304, 2005; and C. Kottler & R. Kaufmann, U.S. Pat. No. 7,924,973.]
It should be noted that other configurations exist in which the object, such as a mouse 240-M, can be placed between the beam splitting grating G1 210-A and the analyzer grating G2 220 and detector 290, as illustrated in FIG. 6. Other configurations using various phase and amplitude gratings, or using detector 290 with higher resolution pixels without the analyzer grating 220, may also be known to those skilled in the art.
Aside from imaging the anatomy of mice, clinical applications of phase-contrast x-ray imaging may be found in mammography, where the density of cancerous tissue may have a distinct phase signature from healthy tissue [see, for example, J. Keyriläinen et al., “Phase contrast X-ray imaging of breast”, Acta Radiologica vol. 51 (8) pp. 866-884, 2010], or for bone diseases like osteoporosis or osteoarthritis, in which the angular orientation of the bone structures may be an early indicator of bone disease [see, for example, P. Coan et al., “In vivo x-ray phase contrast analyzer-based imaging for longitudinal osteoarthritis studies in guinea pigs”, Phys. Med. Biol. vol. 55(24), pp. 7649-62, 2010].
However, for the prior art configurations described so far, x-ray power is a problem. An x-ray source with a full-width half maximum diameter S given by
                    S        ≤                              λ            ⁢                                                  ⁢            L                                2            ⁢            π            ⁢                                                  ⁢                          p              1                                                          [                  Eqn          .                                          ⁢          2                ]            where p1 is the period of the beam splitting grating G1 210 and L the distance between the source 200 and the beam splitting grating G1 210, is required for the technique to produce high contrast fringes and Moiré patterns. For practical applications and system geometries, this implies a microfocus source. However, electron bombardment of the target also causes heating, and the x-ray power that can be achieved is limited by the maximum total electron power that can fall on the microspot without melting the x-ray generating material. A limited electron power means a limited x-ray power, and the low x-ray flux achievable with typical x-ray targets may lead to unacceptable long exposure times when used, for example, for mammography or other diagnostic tests involving live patients or animals. The total x-ray flux can be increased by distributing higher electron power over a larger area, but then the source becomes less coherent, degrading the image contrast.
Coherent x-rays of higher brightness and sufficient flux can be achieved by using a synchrotron or free-electron laser x-ray source, but these machines may occupy facilities that cover acres of land, and are impractical for use in clinical environments.
One innovation that has been shown to enable greater x-ray power employs an additional grating G0 [see, for example, John F. Clauser, U.S. Pat. No. 5,812,629, issued Sep. 22, 1998]. Such a system is illustrated in FIG. 7. In this configuration, a source grating G0 308 with period p0, which is typically an x-ray transmission grating, is used in front of an x-ray source 300. In this case, the x-ray source may be a high-power extended source with a large incident electron beam area (and not a microfocus source) that produces a higher total flux of x-rays.
The x-rays 388 pass through the grating G0 308 and emerge from the grating apertures as an array of individually spatially coherent (similar to a microfocus source described above) but mutually incoherent sub-sources of illumination for the beam splitting grating G1. To ensure that each x-ray sub-source in G0 contributes constructively to the image-formation process, the geometry of the setup should satisfy the condition:
                              p          0                =                              p            2                    ⁢                      L            D                                              [                  Eqn          .                                          ⁢          3                ]            When the condition is met, the x-rays from the many apertures of G0 produce the same (overlapping) Talbot interference pattern, and because the various mutually incoherent sources do not interfere with each other, these Talbot patterns will add as intensities. The effect at the detector 290 is therefore to simply increasing the signal (along with it the signal-to-noise ratio) over what a single coherent source can provide.
This configuration is called the Talbot-Lau interferometer [see Franz Pfeiffer et al., “Phase retrieval and differential phase-contrast imaging with low-brilliance X-ray sources”, Nature Physics vol. 2, pp. 258-261, 2006; and also Described in U.S. Pat. No. 7,889,838 by Christian David, Franz Pfeiffer and Timm Weitkamp, issued Feb. 15, 2011].
FIG. 8 illustrates an example of periodic structures in an object (an IC or silicon wafer) that may be examined using the methods of the invention disclosed herein. This illustration (published in of Victor Vartanian et al., “Metrology needs for through-silicon via fabrication”, in J. Micro/Nanolith. MEMS MOEMS vol. 13(1), 011206 (January-March 2014), FIG. 6) shows a cross section of copper through silicon vias (TSVs) that have been fabricated with voids in the center of the TSV.
Unfortunately, the current art of Talbot-Lau GBIs have many constraints for most practical applications such as semiconductor device inspection, including a requirement that both the source grating G0 and the analyzer grating G2 have fine pitches and apertures with large aspect ratios.
The requirement for the source grating G0 is to create fine individual well-separated x-ray sub-sources to minimize the reduction in image contrast due to unwanted transmission of x-rays through the aperture defining structures. However, for a 1:1 line-to-space ratio grating, simple x-ray shadowing dictates that the x-ray transmission through the grating is limited to less than 50%, and is reduced further when the angular shadowing (limiting the angular range of the x-rays from the source to reach the object) is included. Furthermore, the optimal line-to-space ratio for G0 that reduces the radiation dose to the object (which is important to preclinical and clinical imaging applications) is closer to 3:1 rather than 1:1. In this case, about 75% of the x-rays from the source are blocked due to area shadowing alone, and when gratings with large aspect ratios are used, greater losses occur due to angular shadowing.
The requirement for the analyzer grating G2 is to be able to sample the Talbot interference fringes with sufficient resolution without losing contrast. As a result, both the G0 and G2 gratings must have small apertures and be of thickness sufficient to minimize unwanted x-ray transmission, which limits the efficient use of the x-rays from the source. Furthermore, the loss from the analyzer grating G2 further results in a significantly higher dose (relative to the same system without a G2 grating) for the object under investigation to produce an image with good characteristics due to multiple exposures for phase-stepping and absorption of x-rays resulting in lower signal-to-noise. When the object under investigation is a live animal or human, higher doses of ionizing radiation are undesirable and generally discouraged.
If the aperture dimensions of the grating G0 are larger, angular collimation can be reduced (although not the area shadowing) so that x-ray transmission is not reduced as severely, but this reduces the spatial coherence length of the x-ray beam downstream from the apertures, and leads a reduction in image contrast. Smaller apertures can increase the possible image contrast and resolution by improving spatial coherence, but decreases the overall number of x-rays in the system, thus requiring longer exposure times. Moreover, with smaller apertures, these fine gratings become more difficult to manufacture.
The problem is exacerbated when attempting to use a Talbot-Lau interferometer for higher energy x-rays, which are often desired to obtain sufficient transmission through an object and to reduce radiation dose. In general, as was illustrated in FIG. 1, the absorption of x-rays for biological tissue is far lower for x-rays with energy greater than 5 keV, and the use of higher energy x-rays will reduce the absorbed dose of potentially harmful ionizing radiation by orders of magnitude. However, 5 keV photons have a wavelength of 0.248 nm, and 50 keV have a wavelength 10 times smaller (0.0248 nm). Furthermore, building absorbing gratings such as G0 and G2 for these higher-energy, shorter-wavelength x-rays can present difficulties, as the thickness of the gratings must increase exponentially to maintain the same absorption factor for higher energy x-rays (the x-ray attenuation length is approximately proportional to Ekev3).
The preceding problems of Talbot-Lau GBIs using linear gratings, which can be used for collecting interference data in one dimension only, become more severe if one wishes to generate phase-contrast images in two orthogonal directions. This is often required to make the image reconstruction robust and images more understandable, and because features parallel to the grating lines in the 1-D case are typically less accurately measured. One simple approach is to perform XPCI in two orthogonal directions and then subsequently register the two datasets properly. In addition to challenges associated with the imaging and registration processes, this approach may not be practical, especially when used with living subjects who may move or simply become impatient, and who will incur increased dosage (doubled) if the phase stepping must be performed in two directions. Simultaneous two-dimensional XPCI would be desirable, especially if data collection in a single exposure (shot) and at high x-ray energies is possible to reduce exposure times and the absorbed dosage.
There is therefore a need for an x-ray interferometric imaging system that offers the resolution and detection capabilities of the Talbot-Lau interferometer, but employing a brighter compact source of x-rays and, ideally, a brighter source of higher energy x-rays, especially one that could provide simultaneous two-dimensional phase-contrast imaging.